CSIR-National Chemical Laboratory, Pune – 411008 Crystallography deals with crystals
A crystal is a solid with an orderly, repeating arrangement of atoms
2 Crystals are everywhere!
3
Hexagonal System, Sp. Gp. P63/mmc Crystals are everywhere! Transparent Opaque
Translucent
4 Crystals are everywhere!
5 fibrous
Needles
Prismatic Tabular
6 Crystals found in everyday life
7 Crystals found in everyday life
Diamond Graphite Fullerene
8 Historic definition before the advent of crystallography -A solid with well-defined faces
Crystallographic definition - A material with a regularly repeating structural motif
The strict definition is more vague - Any material that gives diffraction pattern with sharp peaks
9 What is a Crystal?
10 What is not a Crystal?
11 What is a Crystal? A Regular Arrangements of Atoms, Ions or Molecules
12 CLASSIFICATION OF SOLIDS BASED ON ATOMIC ARRANGEMENT
AMORPHOUS QUASICRYSTALS CRYSTALS
Short range order order long range order + + + No periodicity No periodicity periodicity What? Science of the arrangement of atoms in molecules
Science of the arrangement of molecules with respect to each other
Implications for these arrangements for a myriad of areas of science from bioscience to nanotechnology
Not the science of crystals
14 Why?
Materials’ properties are intimately related to their structures
Understanding certain properties requires knowledge of atomic arrangement, e.g. piezoelectric, polarization, optical activity, hardness, compressibility, solubility, colour , density etc.
This technique is essential for chemist’s today for knowledge of accurate molecular structure, which is an essential for structure based functional studies to aid in the development of effective materials.
15 Geometrical Crystallography- Study of external shape of crystal
16 Early thoughts about crystals Symmetry
Crystals are solid - but solids are not necessarily crystalline
Crystals have symmetry (Kepler,1611) and long range order - First speculation on the nature of six-fold symmetry of snowflakes based on the observation that small ice spheres can produce a regular polygon
17 Group discussion
Kepler wondered why snowflakes have 6 corners, never 5 or 7. By considering the packing of polygons in 2 dimensions, demonstrate why pentagons and heptagons shouldn’t occur.
Empty space is not allowed 18
?
Empty space is not allowed ?
Empty space is not allowed Space filling repeat patterns
Only 2, 3, 4 and 6-fold rotations can produce space filling patterns Crystal faces: crystal usually Crystal edge: It is formed by bounded by a number of flat intersection of two adjacent surfaces (faces). faces
Face
4 + 4 + 4 = 12 edge External parts of crystal
Solid angle: It is formed by Interfacial Angle: It is angle between two intersection of more than two adjacent faces. adjacent faces More accurately it is angle locates between two verticals drawn to any two adjacent faces.
Interfacial Angle
4 + 4 = 8 Solid angle Interfacial Angle Law of constant interfacial angles Angles between the crystal faces of a given species are constant Contact (A. Carangeot,1783): To determine the angle between two surfaces, one has to hold the crystal edge at the scissor opening between the limbs of the goniometer. The angle being measured is read from the scale.
Reflecting (W.H. Wollaston, 1809): Instead of measuring the angle formed by the meeting of two faces of a crystal directly, it measured the angle formed by the meeting of rays of light reflected from
them. 29
CRYSTAL SYSTEMS are divided into 7 main groups.
The first group is the ISOMETRIC (Cubic). This literally means “equal measure” and refers to the equal size of the crystal axes. Fluorite Crystals Pyrite Crystals Spinel Fluorite Pyrite Cube with Pyritohedron Octahedron Cube Striations
Garnet Trapezohedron Garnet - Dodecahedron Grossularite, Dodecahedra Three horizontal axes meeting at angles of 120o and one perpendicular axis.
This model represents a hexagonal PRISM (the outside hexagon - six sided shape). The top and bottom faces are called PINACOIDS and are perpendicular to the vertical “c” axis.
BERYL 34 WULFENITE
APOPHYLLITE on Stilbite Topaz from Topaz Mountain, Utah. Pinacoid View
STAUROLITE
Prism View Top View
Mica
Orthoclase Gypsum Microcline, variety Amazonite Abbé René Just Haűy (1743 – 1822): Father of Crystallography
Gabriel Delafosse Auguste Laurent Christian Samuel Weiss
Crystal Structure Model Symmetry in Crystal Bravais, a graduate of the École Polytechnique and a professor of physics, worked out a mathematical theory of crystal symmetry based on the concept of the crystal lattice, of which there were 14. The Unit Cell “The smallest repeat unit of a crystal structure, in 3D, which shows the full symmetry of the structure”
The unit cell is a box with: • 3 sides - a, b, c • 3 angles - , ,
Only 1/8 of each lattice point in a unit cell can actually be assigned to that cell.
Each unit cell in the figure can be associated with 8 x
1/8 = 1 lattice point. 42 Building a crystal
vc
2c ub c 2b b 0 a 2a 3a 4a ta
43 Lattice Crystal Translationally periodic Translationally periodic arrangement of points in arrangement of motifs space
Crystal = Lattice + Motif
Lattice the underlying periodicity of the crystal Basis or Motif atom or group of atoms associated with each lattice points
Lattice how to repeat Motif what to repeat Crystal structure can be obtained by attaching atoms, groups of atoms or molecules which are called basis (motif) to the lattice sides of the lattice point.
+
=
Elemental solids (Argon): Basis = single atom. Polyatomic Elements: Basis = two or four atoms. Complex organic compounds: Basis = thousands of atoms.
Seven unit cell shapes
Triclinic abc 90° Monoclinic abc ==90°, 90° Orthorhombic abc ===90° Tetragonal a=bc ===90° Rhombohedral a=b=c ==90° Hexagonal a=bc ==90°, =120° Cubic a=b=c ===90° The 14 Bravais lattices
Triclinic P Monoclinic P Monoclinic ( C ) a b c, a b c, 90 90 a b c, 90oo , ß 90 The 14 Bravais lattices
Orthorhombic (P) Orthorhombic (C) Orthorhombic (I) Orthorhombic (F) o a b c, =ß= =90 a b c, =ß= =90o a b c, =ß= =90o a b c, =ß= =90o The 14 Bravais lattices
Rhombohedral (R) Trigonal P a=b=c, =ß= 90o Tetragonal (P) Tetragonal (I) Hexagonal (P) oo a=b c, =ß= =90o a=b c, =ß= =90o a=b c, =ß=90 , =120 The 14 Bravais lattices
Cubic (P) Cubic (I) Cubic (F) o a=b=c, =ß= =90o a=b=c, =ß= =90o a=b=c, =ß= =90 “Symmetry elements define the (conceptual) motion of an object in space, the symmetry operation, leads to an arrangement that is indistinguishable from the initial arrangement.‖ Rotation, reflection and inversion operations generate a variety of unique arrangements of lattice points (i.e., a shape structure) in three dimensions. Rotational symmetry
Rotation about an axis: 1, 2, 3, 4 or 6
56 Rotational symmetry
ESCHER’S DRAWING
57 Mirror Plane Symmetry
“Arises when one half of an object is the mirror image of the other half”
m
58 Mirror Symmetry
Right and left hands are identical by reflection through a mirror plane.
Imagine σ as a plane pointing into the page. This mirror plane is the symmetry element.
The motion of taking one hand through the plane to give its reflection is the symmetry operation. Centre of Symmetry (i) “present if you can draw a straight line from any point, through the centre, to an equal distance the other side, and arrive at an identical point”
Centre of symmetry at S
60 The inversion, i
Centre of symmetry ◦ reflection through the centre of the molecule to an equal distance on the opposite site.
Point of inversion, i The combination of all available symmetry operations (32 point groups), together with translation symmetry, within the all available lattices (14 Bravais lattices) lead to 230 Space Groups that describe the only ways in Arthur Moritz Schönflies (1853-1928) which identical objects can be arranged in an infinite lattice. The International Tables list those by symbol and number, together with symmetry operators, origins, reflection conditions, and space group projection diagrams.
Yevgraf Stepanovich Federov (1853-1919) Reflection Plane: Glides
The glide plane is perpendicular to the page.
A glide consists of a reflection followed by a translation. Rotation Axis: Screw William Hyde Wollaston. Barlow’s theories of the properties of crystals were based on the close packing of atoms.‖ Independently of Schönflies and Federov , Barlow derived the 230 space groups.
William T. Hosler, ―Barlow, William,‖ Complete Dictionary of Scientific Biography. 2008. Encyclopedia.com. 20 May, 2012. http://www.encyclopedia.com Nov., 1895: W. Röntgen discovered that when certain substances are exposed to the beam of a cathode ray tube, a new kind of penetrating ray capable of fogging photographic plates even when shielded was emitted –
He called it "x-rays". These x-rays also ionized gases through which they passed.
Bertha Röntgen’s Hand 8 Nov, 1895 Röntgen, director of the physics laboratory. Arnold Sommerfeld, Director of the Institute for Theoretical Physics. Experimental work on wave-nature (and wave length) of x-rays. Paul von Groth, professor of mineralogy, world renowned authority on crystallography and mineralogy. Interested in atomic/molecular meaning of crystal structure. Paul Peter Ewald, student of Sommerfeld, working on propagation of x-rays in single crystals. Max von Laue, Provatdozent in Sommerfeld’s Institute. The first kind of scatter process to be recognised was discovered by Max von Laue who was awarded the Nobel prize for physics in 1914 "for his discovery of Max von Laue the diffraction of X-rays by crystals“. His collaborators Walter Friedrich and Paul Knipping took the picture on the right in 1912. It shows how a beam of X-rays is scattered into a characteristic pattern by a X-ray diffraction pattern of copper crystal. In this case it is copper sulphate. sulphate 69 Optical microscope - to view an enlarged image of an object (dimensions mm)
Image
refocused
Lens
Scattered rays
object
Light X-ray diffraction - to view atoms in a molecule Molecules separated by 1-2 Å 3D electron density map m 1 Angstrom (Å) = 0.00000001 cm a -8 -10 t = 10 cm = 10 m h e m O a crystallographer t i computer c s o o o o o o o o o o oo o o Detector No lens exists which is capable of refocusing X-rays Crystal size < 0.5 mm So the lens is replaced by a computer, a crystallographer and a lot of mathematics X-rays
Ref: Crystal Structure Analysis: A Primer. J. P. Glusker & K. N. Trueblood. Oxford University Press X-Ray Diffraction
W. L. Bragg presented a simple explanation of the diffracted beams from a crystal.
The Bragg derivation is simple but is convincing only since it reproduces the correct result.
Sir W. H. Bragg W. L. Bragg (1890-1971) (1862-1942)
72 X-ray Crystallography – in a nutshell
REFLECTIONS
h k l I σ(I) Bragg’s 0 0 2 3523.1 91.3 FT 0 0 3 -1.4 2.8 law 0 0 4 306.5 9.6 0 0 5 -0.1 4.7 0 0 6 10378.4 179.8 . . REFLECTIONS . h k l F σ(F) 0 0 2 3523.1 91.3 0 0 3 -1.4 2.8 ? Phase Problem ? 0 0 4 306.5 9.6 0 0 5 -0.1 4.7 Direct Method 0 0 6 10378.4 179.8 Heavy Atom . . Method .
Electron density: r(x y z) = 1/V SSS |F(h k l)| exp[–2pi (hx + hy + lz) + i(h k l)] 74 Photos Top: William Henry Bragg (1862 – 1942); Bottom Wlliam Lawrence Bragg (1890-1971) Swedish postage stamp with Braggs ―The most satisfying result was on von Laue’s photograph of diffraction from zinc blende crystals.
Von Laue had assumed that atoms in zinc blende are arranged in a simple cubic lattice, but if this was true Bragg’s law wouldn’t explain the diffraction pattern.
But if the arrangement of atoms was…arranged in a face centred cubic lattice, the diffraction pattern was explained perfectly.‖ 77 The crystal is getting cooled to 120K (-153 ºC, -243 ºF)
78 X-ray Diffractometer:
79 Crystal Structures of Carbon Allotrope
W. L. Bragg (1890-1971)
J. D. Bernal, 1924 Bragg WH, Bragg WL (1913). "The structure of the diamond". Nature 91 (2283): 557 Graphite has a layered structure that Tetrahedral arrangement of C-atoms consists of rings of six carbon and length of C-C bond 1.52 Å atoms arranged in widely spaced horizontal sheets.
Buckminster Fullerene, 1985, H. Kroto
80 Bragg WL (1914). "The Crystalline Structure of Copper". Phil. Mag. 28 (165): 355
Bragg WL (1914). "The analysis of crystals by the X-ray spectrometer". Proc. R. Soc. Lond. A89 (613): 468
81 Bragg WH (1915). "The structure of the spinel group of crystals". Phil. Mag. 30 (176): 305.
Vegard L (1916). "Results of Crystal Analysis". Phil. Mag. 32 (187): 65.)
82 Bragg WL (1920). "The crystalline structure of zinc oxide". Phil. Mag. 39 (234): 647.)
83 Application to Organic Compounds
In 1923: The first Structure of an Organic compound, Hexamethylenetetramine, was solved in 1923 by Dickinson and Raymond. This was followed by several studies of long-chain fatty acids, which are an important component of biological membranes. Earlier, Assumption about benzene structure
The molecule exists in the crystal as a separate entity.
The benzene carbon atoms are arranged in ring formation.
The ring is hexagonal or pseudo-hexagonal in shape.
The above reasoning, in fact, supplies a definite proof, from an X-ray point of view, that the chemist's conception of the benzene ring is a true representation of the facts.‖ Hexamethylbenzene established the hexagonal symmetry of benzene and showed a clear difference in bond length between the aliphatic C–C bonds and aromatic C–C bonds; this finding led to the idea of resonance between chemical bonds, which had profound consequences for the development of chemistry.
Lonsdale K (1928). "The structure of the benzene ring". Nature 122 (3082): 810.Bibcode:1928Natur.122 Understanding the molecular structure of wool - the changing shape of keratin
The principal component of hair is a protein molecule called keratin. All protein molecules consist of long chains of small molecular units, the amino acids, of which there are 20 different kinds. Each keratin molecule in hair consists of many hundreds of amino acid units, arranged in an irregular order, although not a random one by analogy, the letters in this sentence are in an irregular order, but the sentence has meaning. The order in keratin determines how the molecules fit together, giving the hair strength and flexibility.
The long chains of keratin could be compacted, called the alpha-form (shown left) or stretched out, called the beta-form (shown right). Using his X-ray analysis, Astbury showed that the elasticity or stretchiness of wool fibres was due to the compacted alpha-keratin protein fibres
unfolding into the more extended beta-form. 87 William Thomas Astbury 1898-1961
Whilst this discovery was of great interest to the textile industry, its real significance was that it showed how the macroscopic properties of biological materials could be understood in terms of changes in the shape of their constituent protein molecules. This was to lead to a novel approach to understanding biological systems, that Astbury referred to as molecular biology. First to determine the three-dimensional structure of a complex bio-organic molecule.
She determined the structure of cholesteryl iodide by x- ray diffraction in 1941-42 (published in 1945) in complete three-dimensional detail, at a time when no one else was determining complex structures in three dimensions because of the formidable calculations involved.
89 Determined the structure of penicillin in 1944 (published in 1949), again in three-dimensional detail. Before her work there was only fragmentary and conflicting evidence on the structure, from chemical analysis, of this rather unstable molecule, which was of immense importance as an antibiotic during and immediately after World War II.
Determined the structure of vitamin B-12 in 1956, using one of the first high-speed digital computers. This was by far the most complex molecule whose three-dimensional architecture had been established, and some of its unusual structural features were quite unanticipated. 90 Determined the structure of insulin in 1969. This culminated a study pursued over three decades. The details of the structure provided insight into the function of this vital hormone.
91 Myoglobin Hemoglobin
Structure solved in 1950 Structure solved in 1959 by John Kendrew by Max Perutz
Both shared 1962 Nobel Prize for Chemistry
92 In 1937 William Astbury produced the first X-ray diffraction patterns that showed that DNA had a regular structure He was pioneer in the field of DNA research
Astbury W, (1947). "Nucleic acid". Symp. SOC. Exp. Biol. 1 (66).
X-ray diffraction image of the double helix structure of the DNA molecule, Sir William Astbury taken 1952 by Raymond Gosling, commonly referred to as "Photo 51", during work by Rosalind Franklin on the structure of DNA James Watson & Francis Crick
In 1953, James Watson and Francis Crick suggested what is now accepted as the first correct double-helix model of DNA structure in the journal Nature. Their double-helix, molecular model of DNA was then based on a single X-ray diffraction image (labeled as "Photo 51") taken by Rosalind Franklin and Raymond Gosling in May 1952, as well as the information that the DNA bases are paired — also obtained through private communications from Erwin Chargaff in the previous years. Solving the Structure of DNA
Watson J.D. and Crick F.H.C. (1953). "A Structure for Deoxyribose Nucleic Acid" (PDF). Nature 171 (4356): 737–738. Bibcode:1953Natur.171..737W Solving the Structure of DNA
Watson and Crick’s DNA model
In 1962 James Watson, Francis Crick, and Maurice Wilkins jointly received the Nobel Prize in physiology or medicine for their 1953 determination of the structure DNA. Triple Helix structure of collagen and Ramchandran plot
Prof. G. N. Ramchandran,
Venkatraman Ramakrishnan W. L. Bragg
99 Structure of few anti-cancer drugs 100 BCR-ABL kinase domain: showing the binding pocket of nilotinib (purple) bound to the active site of the target BCR-ABL in Chain C. In this figure, BCR-ABL is the cluster of four chains (chain A , chain B [purple], chain C [blue], and chain D [red]). 101 The tyrosine kinase domain of the EGF receptor: showing the binding of gefitinib. 102 Binding pocket of Sunitinib in the TRK KIT. Binding of sitagliptin within DPP-IV. The ability of a compound to exist in more than one crystal form i.e. different molecular arrangements in the crystal lattice.
• Packing Polymorph • Conformational Polymorph Paracetamol
Orthorhombic (Pbca) Monoclinic(P21/c)
J. Pharm. Sci., 1983, 72, 232 105 Conformational Polymorph Ritonavir
Form I Form II Form I – red, Form II - blue
Morris, J. et al. Pharmaceutical Research, Vol. 18, No. 6, 2001 Retonavir Polymorphs: Difference in Molecular Arrangements
Form I Form II . In Chocolates:
Cocoa butter - The main ingredient of chocolate.
The fats in cocoa butter can crystallize in six different forms. The six different crystal forms have different properties. Conformational Polymorphism Cyclo tetramethylene tetranitramine (HMX)
NO2
N -Form: Blue Four polymorphs known, , -Form: Red N NO2 , , ; form is least O2N N -Form: Green stable whereas form is N most stable -Form: Orange
NO2
Form Form Form Form Cyclo tetramethylene tetranitramine (HMX)
Form Form
Form Form Cocrystal Design
What is Cocrystal?
A + B A-B
A crystal containing two or more neutral solid component together
Carbamazepine – succinic acid theophylline – nicotinamide
Why cocrystal?
Cocrystal generates different crystalline form of a compound.
Modify significant properties
◊ Solubility
◊ Dissolution rate
◊ Bioavailability
◊ Chemical stability
◊ Moisture uptake
◊ Mechanical behavior
Intellectual property and patents Cocrystals One of the components of a cocrystal may serve as a co- crystal former. The components interact via non-covalent interactions such as hydrogen bonding, ionic interactions, van der Waals interactions and p-stacking interactions.
Realizing the Benefits
Case Study 1
Cocrystals Screening Based on Paracetamol Two Molecules Possess an almost identical conformation
O CH 3 Form I HO N on top of H form II
Form I
Side View
Form II Compaction Property Screening for Compressible Cocrystals
The aim therefore was to prepare various cocrystals of paracetamol and study mechanical properties with a view to being able to form tablets
How to select possible cocrystal formers? And how to screen?
They selected 20 selected possible cocrystal formers
Used the simple method of grinding and liquid assisted grinding to screen for cocrystallisation. Range of cocrystal formers Crystal Packing of Paracetamol-Oxalic Acid Cocrystal Crystal Packing of Paracetamol-Oxalic Acid Cocrystal Case Study 2 Example of Caffeine Hydration
Bulk stability in the context of hydrate formation. How to ―stabilise‖ a molecule that otherwise crystallizes in an unstable/reactive form?
Picks up water from the atmosphere to form the hydrate. Properties will therefore change. Cocrystal Designing Caffeine Cocrystal
Caffeine: OA Caffeine: MA 2 : 1 2 : 1 Prof. G. R. Desiraju
The understanding of intermolecular interactions in the context of crystal packing and the utilization of such understanding in the design of new solids with desired physical and chemical properties
129 130 131 132 Introduction to Advanced Porous Crystalline Materials
Zeolites Metal-organic framework Covalent-organic framework
Zeolites MOFs COFs Discovery 1756 1995 2005 Pore size <1 nm 0.3 nm to 10 nm 0.7 nm to 5 nm Surface area 904 m2g-1 7000 m2g-1 4650 m2g-1 Functionality No Yes Yes Stability High Low-Moderate Moderate-High Applications Adsorption, catalysis, Multifunctional Multifunctional etc. materials materials 133 Yaghi et al., J. Am. Chem. SOC. 1995,117, 10401, Cote et al., Science, 2005, 310, 1166. Metal-organic frameworks (MOFs) Example of Metal-organic frameworks (MOFs)
DEF (12mL) H2BDC + Zn(NO3)24H2O Zn4O(BDC)3(DEF)7
Zn4O(O2C-C6H4-CO2)3: MOF-5 Different doped MOF crystals 135 H. Li, M. Eddaoudi, M. O'Keeffe, O. M. Yaghi. Nature (1999) 402, 276-279 General Route for MOF Synthesis Applications of Metal-organic frameworks (MOFs) Covalent Organic Frameworks
138 Cote et al. Science, 2005, 310, 1166-1170 Linkers used for Covalent Organic Frameworks Synthesis and Applications of COFs
Solvothermal Ionothermal Mechanochemical Microwave Growth on template
Biswal et al., J. Am. Chem. Soc., 2013, 135, 5328. Dichtel et al., Science, 2011, 332, 228. 2) Photoconducting material 1) Gas storage (H2, CO2, CH4, NH3)
3) Heterogeneous catalysis
15 mol /kg, at 298 K, 1 bar 140 140 Doonan et al., Nat. Chem., 2010, 2, 235. Wang et al., J. Am. Chem. Soc., 2011, 133, 1981. 141 • W. C. Röntgen 1901 Discovery of X-rays (Physics) • M. Von Laue 1914 Diffraction of X-rays by crystals (Physics) • W.H. Bragg & W.L. Bragg 1915 Use of X-rays to determine crystal structure (Physics) • Charles Glover Barkla 1917 Discovery of the characteristic Röntgen radiation of the elements (Physics) • A. H. Compton 1927 Physics, Scattering of X-rays by electrons (Physics) • Louis-Victor de Broglie 1929 Wave nature of the electron (Physics) • C. J. Davisson, G. P. Thomson 1936 Diffraction of electrons by crystals (Physics) • J.B. Sumner 1946 For his discovery that enzymes can be crystallized (Chemistry) • L. C. Pauling 1954 Nature of chemical bond and its application in structure of complex substances (C) • Perutz and Kendrew 1962 For determining the structure of globular proteins (Chemistry) • Crick, Watson and Wilkens 1962 Medicine, Double Helix (Physiology or Medicine) • D..Hodgkin 1964 Structure of vitamin B, Penicillin (Chemistry) • Barton and Hassel 1969 Concept of conformation (Chemistry) • C.B. Anfinsen 1972 Folding of protein chains (Chemistry) • Lipscomb 1976 Structure of boranes (Chemistry) • A. Klug 1982 Crystallographic electron microscopy and nuclei acid-protein complexes (C) • Hauptmann & Karle 1985 Development of direct methods for the determination of crystal structures (C) • J. Deisenhofer, R. Huber, H. Michel 1988 Determination of the 3D structure of a photosynthetic reaction center (C) • Pierre-Gilles de Gennes 1991 Methods of discovering order in simple systems can be applied to polymers & LC (P) • Georges Charpak 1992 Discovery of the multi wire proportional chamber (Physics) • C. G. Shull, B. N. Brockhouse 1994 For their pioneering research in neutron scattering (Physics) • R. F. Curl, H. W. Kroto, R. E. Smalley 1996 For their discovery of the fullerene form of carbon (Chemistry) • P.D. Boyer, J.E. Walker, J.C. Skou 1997 Elucidation of the enzymatic mechanism underlying the synthesis of adenosine triphosphate (ATP) and discovery of an ion-transporting enzyme (C) • R. MacKinnon 2003 Potassium Channels (Chemistry) • R.D. Kornberg 2006 Studies of the molecular basis of eukaryotic transcription (Chemistry) • V. Ramakrishnan, T.A. Steitz, A.E. Yonath 2009 Studies of the structure and function of the ribosome (Chemistry) • D. Shechtman 2011 For the discovery of quasicrystals (Chemistry) Dorothy Hodgkin – (1910-1994)
143